Ship Design - Main Dimensions

5. ESTIMATION OF DISPLACEMENT AND MAIN DIMENSIONS General design characteristics of a ship may be described in three main groups • • •

The displacement The main dimensions, and The hull form

In this chapter we will deal with the estimation of size and main dimensions during the early stages of ship design.

5.1. The Displacement of a Ship The displacement is the weight of the ship, which is equivalent to the weight of water displaced by the ship as it floats. Light ship is the weight of the ship and its permanent equipment. Load displacement is the weight of the ship when it is filled with fuel and cargo to its designed capacity, that is, when it is immersed to its load line. The displacement tonnage is

∆ = DWT + LS Where DWT is the Deadweight tonnage and LS indicates the Lightship weight. Light ship displacement is the weight of the ship excluding cargo, fuel, ballast, stores, passengers and crew. The main components of the light ship are the weight of structure, outfit, main and auxiliary machinery, and other equipment. Deadweight tonnage is the weight, in metric tons, of the cargo, stores, fuel, passengers, and crew carried when the ship is immersed to its maximum summer load line. Cargo deadweight refers to the revenue generating cargo capacity of a ship and is determined by deducting the weight of fuel, water, stores, crew, passengers and other items necessary for voyage from the deadweight tonnage. The ratio of the deadweight at the load draught to the corresponding displacement is termed the deadweight coefficient

CD =

DWT ∆

Typical values of CD for different ship types are presented in Table 5.1. Table 5.1. DWT/∆ ratios for merchant ships Ship type CD Passenger ship 0.35 General cargo ship 0.62-0.72 Large bulk carrier 0.78-0.84 Small bulk carrier 0.71-0.77 Container ship 0.70-0.75 Oil tanker 0.80-0.86 Product tanker 0.77-0.83 Ro-Ro 0.50-0.59 Trawler 0.37-0.45 LPG carrier 0.62 Kafalı (1988) recommends the following formulae for small cargo ships and tankers Tanker Cargo Ship

DWT 0.775DWT = ∆ DWT + 250 DWT 0.750DWT = ∆ DWT + 300 5.1

5.2. Main Dimensions The main dimensions (L, B, T, D) affect the many techno-economical performance characteristics of a ship. Therefore the proper selection of the main dimensions is vitally important in the early stages of design. There may be an infinite number of combinations of length, breadth, depth and draught, which satisfy the main requirements, and restrictions of the design problem. The designer will attempt to find the best combination, however there are too many factors to be investigated within a limited time period. Therefore, the designer, most commonly, will use an iterative approach and the resultant main dimensions will be a compromise solution rather than the optimum values. The estimation of main dimensions will require an iterative process based on the following order • • • •

Estimate the design displacement. Estimate length based on displacement and speed Estimate breadth based on length Estimate block coefficient based on length and speed

• •

Calculate draught to satisfy ∆ = LBTC B Calculate the required freeboard and hence the minimum required depth

Dimensional constraints may impose a limit on length, breadth, draught and air draught. A constraint on length may be set by the dimensions of canal locks or docks. It may also be set by a need to be able to turn the ship in a narrow waterway. The constrained length is usually the overall length but in some cases the constraint may apply at the waterline at which the ship is floating. A limit on breadth is usually set by canal or dock lock gates, but the breadth of vehicle ferries is sometimes limited by the dimensions and position of shore ramps giving vehicles access to bow or stern doors. The outreach of other shore based cargo handling devices such as grain elevators or coal hoists can limit the desirable distance of the offshore hatch side from the dockside and thereby limit the breadth of the ship. A draught limit is usually set by the depth of water in the ports and approaches to which the ship is intended to trade. For very large tankers the depth of the sea itself must be considered. The air draught of a ship is the vertical distance from the waterline to the highest point of the ship’s structure and denotes the ship’s ability to pass under a bridge or other obstruction, which forms part of the projected route. Table 5.2. Dimensional restraints Max length (m) Max breadth (m) Max draught (m) Air draught (m) Suez 74.0 11.0 48.0 17.7 Panama 289.6 (950 feet) 32.2 (106 feet) 12.04 TFW (39.5 57.91 (190 feet) feet) St Lawrence 228.6 22.86 8.0 35.5 Kiel 315 40 9.5 -

5.2.1. Length The length of a ship will affect most of the technical and economical performance requirements. The following will be observed when two ships with the same displacement but with different length values are compared. •

•

The longer ship will have larger wetted surface area and hence higher viscous resistance. However, both the wave making resistance and the propulsive performance will improve with and increasing length. Therefore, fast ships should have higher lengths compared with slow speed vessels. Both the weight and building cost of ship will increase with length. 5.2

• • • • • •

Long ships may achieve the same speed with less engine power; hence the increasing length will reduce the operational costs. Increasing length with constant displacement may result in losses in capacity Increasing length may detoriate the intact stability characteristics. Increasing length will improve the directional stability but worsen the turning ability Increasing length will require a higher value of freeboard Increasing length will improve the vertical plane motions, including heave, pitch, vertical accelerations, deck wetness and probability of slamming

Many empirical formulae have been proposed to estimate the design length. These formulae are usually based on displacement and design speed. Ayre ( )

 10 5 V  L = ∆1 / 3  +   3 3 L where L[m], ∆[ton] and V[knot]. Posdunine ( ) 2

 V  1/ 3 L = C  ∆ V + 2 where L[m], ∆[ton] and V[knot]. C coefficient is recommended as follows Single screw ships Twin screw ships (slow speed) Twin screw ships (high speed)

Watson (1962) 7.15 7.30 7.90

Parsons (1994) 7.1 – 7.4 (11-16.5 knots) 7.4 – 7.7 (15-20 knots) 8.0 – 9.7 (20-30 knots)

Baxter (1976) 7.13 7.28 7.88

Schneekluth reccommends C=7.25 for freighters with a trial speed of 15.5 to 18.5 knots. Kafalı (1988) proposes the following values for C coefficient.

C=3

V

+ 3.2 L V C = 1.7 + 4.4 L V C = 0.75 + 3.66 L

Passenger ship Cargo ship - tanker Tug

where V (knot) and L (m) Gilfillan (1968) proposes the following formula for the length of a bulk carrier

 V  1/ 3 L = 7.38 DWT V + 2 Völker ( ) proposes the following formula for dry cargo and container ships

 V L = ∆1 / 3  3.5 + 2.3  g∆1 / 3 

   

Where L[m], ∆[ton] and V[knot] . Schneekluth (1987) developed the following formula on the basis of lowest production costs.

L = C∆0.3 V 0.3 5.3

Where L[m], ∆[ton] and V[knot] . C is a coefficient which van be taken 3.2 if the block coefficient has the approximate value of C B =

0.145 within the range of 0.48-0.85. If the block coefficient differs Fn

from this value the coefficient C can be modified as follows

C = 3 .2

Where

Fn =

V gL

C B + 0 .5 0.145 + 0 .5 Fn

(L [m], V [m/s])

Benford(10) recommends the following formula for liner type general cargo vessels:

 V  1/ 3 L = 6.31 ∆ V + 2

V [knot]

Wright () proposes the following formula for the design length

L BP = 5.58 DWT1 / 3  V  1/ 3 DWT and ship design length has been investigated for a V + 2  

The relation between the term 

large number of recent designs which resulted in a series of empirical formulae as given in the following table. Ship type Container Tanker Chemical tanker

Design length (m)

 V  1/ 3 8.13 DWT − 33.975 V +2  V  1/ 3 5.31 DWT + 14.743 V 2 +    V  1/ 3 5.11 DWT + 16.945 V+ 2

Ship type General Cargo Bulk carrier

Design length (m)

 V  1/ 3 5.54 DWT + 12.041 V + 2  V  1/ 3 5.38 DWT + 15.461 + V 2  

Example 5.1. Estimate the length of a ship with a displacement of 1000 ton and a design speed of 10 knots by using the Ayre formula. Solution: The Ayre formula will require and iterative approach as shown in the following table Displacement 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

Speed 10 10 10 10 10 10 10 10 10 10

L

100.0000 50.0000 56.9036 55.4276 55.7198 55.6610 55.6728 55.6704 55.6709 55.6708

 10 5 V  ∆1 / 3  +   3 3 L 50.0000 56.9036 55.4276 55.7198 55.6610 55.6728 55.6705 55.6709 55.6708 55.6708

5.4

This process can also be carried out graphically as shown below. 100 90 80 70 Boy

60 50 40 30 20 10 0 0

10

20

30

40

50

60

70

80

90

100

Boy

Example 5.2. Estimate the length of a ship with displacement 1000 t and speed 10 knots by using Posdunine’s formula. C will be taken as C = 1.7

V L

+ 4.4

Solution Displacement

Speed

1000 1000 1000 1000 1000 1000 1000 1000

2

L

 V  1/ 3 C  ∆ V + 2

10 10 10 10 10 10 10 10

100.000 42.361 48.694 47.474 47.690 47.651 47.658 47.657

42.361 48.694 47.474 47.690 47.651 47.658 47.657 47.657

The same result can be obtained graphically as follows: 100 90 80 70 Boy

60 50 40 30 20 10 0 0

10

20

30

40

50

60

70

80

90

100

Boy

Example 5.3. Estimate the length for ships with displacement between 1000-10000 t and design speed 10-15 knot by using Ayre, Posdunine, Völker and Schneekluth formulae. Solution:

5.5

∆ 1000 1000 1000 1000 1000 1000 2000 2000 2000 2000 2000 2000 3000 3000 3000 3000 3000 3000 4000 4000 4000 4000 4000 4000 5000 5000 5000 5000 5000 5000 6000 6000 6000 6000 6000 6000 7000 7000 7000 7000 7000 7000 8000 8000 8000 8000 8000 8000 9000 9000 9000 9000 9000 9000 10000 10000 10000 10000 10000 10000

Speed 10 11 12 13 14 15 10 11 12 13 14 15 10 11 12 13 14 15 10 11 12 13 14 15 10 11 12 13 14 15 10 11 12 13 14 15 10 11 12 13 14 15 10 11 12 13 14 15 10 11 12 13 14 15 10 11 12 13 14 15

Ayre

Posdunine

55,6708 57,5088 59,3042 61,0608 62,7817 64,4694 67,5472 69,6706 71,7464 73,7786 75,7704 77,7249 75,7021 78,0116 80,2703 82,4824 84,6513 86,7802 82,1103 84,5611 86,9589 89,3077 91,6114 93,8730 87,4715 90,0376 92,5488 95,0093 97,4229 99,7929 92,1241 94,7882 97,3958 99,9512 102,4584 104,9207 96,2600 99,0097 101,7016 104,3401 106,9290 109,4719 100,0000 102,8260 105,5929 108,3054 110,9672 113,5820 103,4253 106,3202 109,1550 111,9343 114,6622 117,3420 106,5935 109,5514 112,4483 115,2887 118,0769 120,8162

Schneekluth

47,6567 50,3682 52,9278 55,3590 57,6802 59,9062 58,0241 61,2461 64,2814 67,1593 69,9029 72,5302 65,1614 68,7276 72,0831 75,2611 78,2878 81,1840 70,7791 74,6127 78,2165 81,6271 84,8731 87,9771 75,4845 79,5400 83,3497 86,9528 90,3801 93,6560 79,5718 83,8185 87,8055 91,5743 95,1576 98,5812 83,2080 87,6238 91,7674 95,6826 99,4035 102,9574 86,4982 91,0662 95,3507 99,3974 103,2420 106,9129 89,5133 94,2201 98,6330 102,7995 106,7568 110,5342 92,3034 97,1381 101,6694 105,9463 110,0072 113,8826

Völker

50,7166 52,1877 53,5679 54,8698 56,1033 57,2766 62,4394 64,2506 65,9498 67,5526 69,0713 70,5158 70,5158 72,5612 74,4802 76,2903 78,0054 79,6368 76,8720 79,1017 81,1937 83,1670 85,0367 86,8151 82,1942 84,5783 86,8151 88,9250 90,9242 92,8257 86,8151 89,3333 91,6959 93,9244 96,0359 98,0444 90,9242 93,5615 96,0359 98,3700 100,5814 102,6850 94,6405 97,3856 99,9612 102,3906 104,6925 106,8820 98,0444 100,8883 103,5565 106,0732 108,4579 110,7261 101,1929 104,1281 106,8820 109,4796 111,9408 114,2819

58,2258 60,5484 62,8710 65,1936 67,5161 69,8387 70,1673 72,7743 75,3813 77,9884 80,5954 83,2024 78,3715 81,1607 83,9500 86,7393 89,5286 92,3178 84,8217 87,7480 90,6743 93,6005 96,5268 99,4531 90,2206 93,2578 96,2949 99,3321 102,3692 105,4064 94,9078 98,0386 101,1695 104,3003 107,4312 110,5620 99,0759 102,2883 105,5006 108,7129 111,9253 115,1376 102,8463 106,1309 109,4155 112,7001 115,9848 119,2694 106,3004 109,6501 112,9998 116,3496 119,6993 123,0491 109,4960 112,9051 116,3142 119,7233 123,1324 126,5415

120

Length (m)

100

80 10000 9000 8000 7000 6000 D is 5000 pla 4000 cem 3000 ent 20001000 (t

)

60

10

11

12

S peed

13

14

15

) (knots

5.6

5.2.2. Breadth The effects of breadth on techno-eceonomic performance characteristics of a ship can be summarized as follows. • • • •

Increasing breadth will increase the resistance and hence the engine power and operating costs Increasing breadth will improve the initial stability characteristics. The weight and cost of hull will increase with increasing breadth Roll period will reduce with increasing breadth

The breadth of conventional ship types may be estimated based on the length as shown in the following formulae Ship Type Passenger ship General cargo

Tanker

VLCC

Bulk carrier Containership RoRo Tug

Formula

L + 6.1 9 L + 4.27 9 0.125L + 2.45 L + 6 to 7.5 9 L + 1.98 7.5 0.125L + 2.45 L + 4.5 to 6.5 9 L + 12 to 15 9 L − 14 5 0.146L − 1.04 0.150L + 2.45 L +8 10 0.200L + 2.45 0.220L + 1.50

Proposed by

(Munro-Smith)

(Munro-Smith)

(Munro-Smith)

The breadth of containerships can be estimated on the basis of the number of containers located transversely in the ship. The standard ISO container has a width of 2.44 m. However, each container requires an allowance for clearence, guides etc. of about 240 mm so that each container requires a width of 2.68 m. Thus the number n of cells located transversely in the ship require 2.68n metres. Since the width available for containers is about 80 percent of the ship’s breadth, then B=3.35n.

5.2.3. Draught Draught of a ship is less effective on technical and economical performance compared with length or breadth. Therefore the draught is usually selected to satisfy the displacement equation ∇ = LBTC B . The draught may be limited due to the depths of port, harbour and canals. Low draught increases the risk of bow slamming in rough seas.

5.7

5.2.4. Depth Depth of a ship may be estimated as the sum of design draught and the freeboard. The weight and cost of the ship will increase with increasing depth. Classification Societies may impose certain limits on L/D ratio due to the longitudinal strength characteristics. However lower values of L/D may result in buckling problems. The depth will increase the height of centre of gravity which will affect the stability and seakeeping characteristics of the vessel. The following formulae may be suggested for an initial estimate of depth. Ship Type Passenger ship Cargo

Tanker

Bulk carrier

Containership Frigate

Formula

B + 0.3 1.5 B−2 D= 1.4 B D= 1.65 L D= 13.5 L D= 12.5 B D= 1.9 T D= 0.78 B−3 D= 1.5 B D= 1.9 T D= 0.73 L D= 11.5 B D= 1.7 T D= 0.46 L D= 13.3

Proposed by

D=

Watson (1998)

Watson (1998) Watson (1998) Watson (1998) Munro-Smith Watson (1998) Watson (1998) Watson (1998) Watson (1998) Watson (1998) Watson (1998)

L, B, D in meters. The depth of a container ship is in general controlled by the number of containers to be carried in the hold. Thus

D = 2.43n + h where n is the number of tiers of containers in holds and h is the height of double bottom.

5.8

5.2.5. Length to Beam Ratio L/B ratio affects powering and directional stability. A steady decrease in L/B in recent years can be seen in an effort to reduce ship cost and with increased design effort to produce good inflow to the propeller with the greater beam. Watson&Gilfillan (1977) proposes the following values

L = 6.5 B L = 4.0 + 0.025(L − 30) B L = 4.0 B

L ≥ 130 m 30 ≤ L ≤ 130 m L ≤ 30 m

5.2.6. Length to Depth Ratio L/D ratio is a primary factor in longitudinal strength. Classification Societies, in general, require special consideration L/D>15.

5.2.7. Beam to Depth Ratio B/D ratio has a major impact on stability.

5.2.8. Beam to Draught Ratio If this ratio is too small stability may be a problem; too large residuary resistance goes up.

 B   min CS = 5.93 − 3.33C M T

 B   = 9.625 − 7.5C B  T  max

Example 5.4. Estimate the dimensions of a dry cargo ship of 13000 tonnes DWT at a maximum draught of 8.0 m and with a service speed of 15 knots. Assume CD=0.67 and CB=0.7. Solution:

DWT 13000 = = 19403 t CD 0.67

Displacement

∆=

Length (Ayre)

 10 5 V  L = ∆1 / 3  +   3 3 L

⇒

L = 145.25 m

2

Length (Posdunine) Length (average) Breadth Draught

Depth

Depth (average)

 V  1/ 3 ⇒ L = 149.6 m with C=7.15 L = C  ∆ V + 2 L = 147.425 m L B = + 6 = 22.38 m 9 ∇ 19403 / 1.025 T= = = 8.2 m LBC B 147.425 × 22.38 × 0.7 B−2 D= = 14.56 m 1.4 B D= = 13.56 m 1.65 D = 14.06 m

5.9

Marine Design

34

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This relation must be solved iteratively. Assume a value for LBP and put it into the RHS. Hence evaluate the LHS and arrive at a value for LBP say LBP'. Put this value into the RHS and find a new value for LBP say LBP''. Compare LBP'' with LBP'. When the difference between the two values is sufficiently small then take LBP = LBP''. It must be said that it is not so easy to "fine tune" the Ayre formula to a particular basis ship because it uses two numeric coefficients and it is not obvious whether one alone should be adjusted, or both. However it appears to give initial estimates of length which are consistent with modern practice despite its age. It is therefore still quite useful to the designer.

5.7

Block Coefficient

The variation of Block Coefficient, CB, with Speed and Length is shown in a diagram taken from ‘Practical Ship Design’ by D. G. M. Watson (based on a Figure in the1977 RINA Paper by Watson & Gilfillan). Over the years segments of the curve appropriate to particular ship types have been presented as linear relationships known as "Alexander Formulae" of the form: CB = K - 0.5 V/ √Lf

or

CB = K - 1.68 Fn

where K varies from 1.12 to 1.03 depending on V/ √Lf or Fn and

V is speed in knots, Lf is length in feet v is speed in metres/second, L is length in metres 2 g is acceleration due to gravity in metres/second

The mean line shown in the diagram can be approximated by the equation:CB = 0.7 + 0.125 tan-1((23-100Fn)/4) where the term in brackets is taken in radians.

___________________________________________________________________________ September 2005